Aye Aye Cho, Jing Wang, Da-jun Zhang, “Discretization of the modified Korteweg–de Vries–sine Gordon equation”, TMF, 2023, Volume 217, Number 2,Pages <nobr>329

This article is cited in 1 paper

Discretization of the modified Korteweg–de Vries–sine Gordon equation

Aye Aye Cho^a, Jing Wang^a, Da-jun Zhang^ba

^a Department of Mathematics, Shanghai University, Shanghai, China
^b Newtouch Center for Mathematics of Shanghai University, Shanghai, China

Abstract: We provide an integrable discretization of the modified Korteweg–de Vries–sine Gordon equation. The discrete form is a coupled system and is derived via the Cauchy matrix approach by introducing suitable discrete plane wave factors. Solutions and a Lax pair are constructed in this approach. The dynamics of some solutions are illustrated. The modified Korteweg–de Vries–sine Gordon equation is recovered in the continuum limit.

Keywords: modified Korteweg–de Vries–sine Gordon equation, Cauchy matrix approach, solution, Lax pair, continuum limit.

PACS: 02.30.Ik, 05.45.Yv

MSC: 35Q51, 35Q55, 37K60

Received: 11.02.2023
Revised: 25.05.2023

DOI: 10.4213/tmf10479